Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binarySearch (arr, l, r, x): 
    if r >= l: 
        mid = l + (r - l)//2
        if arr[mid] == x: 
            return mid 
        elif arr[mid] > x: 
            return binarySearch(arr, l, mid-1, x) 
        else: 
            return binarySearch(arr, mid + 1, r, x) 
    else: 
        return -1
n=int(input())
i=t=1
a=[]
x=0
while(x<1000000000):
    x=i*(i+1)
    x//=2
    a.append(x)
    i+=1
for i in a:
    x=n-i
    if(binarySearch(a,0,len(a),x)!=-1):
        print("YES")
        t=0
        break
if(t==1):
    print("NO")